Problem: Simplify the following expression: $\sqrt{75}-\sqrt{27}+\sqrt{48}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{75}-\sqrt{27}+\sqrt{48}$ $= \sqrt{25 \cdot 3}-\sqrt{9 \cdot 3}+\sqrt{16 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{3}-\sqrt{9} \cdot \sqrt{3}+\sqrt{16} \cdot \sqrt{3}$ $= 5\sqrt{3}-3\sqrt{3}+4\sqrt{3}$ Finally, simplify by combining the terms. $= ( 5 - 3 + 4 )\sqrt{3} = 6\sqrt{3}$